In the longitudinal equilibrium pinch shown schematically in Fig. 1, assume that the radial dependence of the current density J_z(r) is such that

Calculate p(r) and B_θ(r) and make a plot showing their radial dependence. Show that, as a → b, the magnetic pressure B_θ²/2μ₀ at r = b becomes equal to p at r = 0, while as a → 0, B_θ²/μ₀ at r = b becomes equal to p at r = 0.

Figure 1.

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J₂ = 0 J₂ = Jo= constant, for J₂ = 0 for for 0 b